Question

What are the next two terms of the following sequence? -2, 4, -8, 16, ...

Answer 1

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

`\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}`

What are the next two terms of the following sequence?

`\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}`

The next two terms are -32 and 64.

`\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}`

First of all, let's identify what kind of sequence this is.

The two main types of sequences are:

• 
  `\textsf{Arithmetic.}` This is where we add/subtract the same number to get to the following term.
• 
  `\textsf{Geometric.}` This is where we multiply/divide by the same number to get to the next term.

In the given sequence, we use multiplication, so we're dealing with a
`\textit{geometric sequence}`.

In order to get to the next term, we multiply by -2.

So in order to find the next two terms of the sequence, we take the previous term and multiply it by -2 as follows:

16•(-2)=-32

We've found the 5th term of the geometic sequence.

Now let's find the 6th:

-32•(-2)=64 (the product of a negative and a negative results in a positive)

Summary of Final Answer:-

The next two terms in the sequence are -32 and 64.

Good luck.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer 2

-32 , 64

Explanation:

Geometric sequence

This is a geometric sequaence and each term is obtatained by multiplying the previous number with the common ratio 'r'

`\sf \boxed{r = (second \ term )/(first \ term)}`

`\sf r =(4)/((-2))`

r = -2

The next two terms ,

Fifth term = 16 *(-2) = -32

Sixth term = (-32) * (-2) = 64